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Necessary conditions for weak efficiency for nonsmooth degenerate multiobjective optimization problems

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Abstract

In this paper we give primal first and second-order necessary conditions for the existence of a local weak minimum for nonsmooth multiobjective optimization problems with inequality constraints and an arbitrary constraint set. For nonsmooth multiobjective problems with inequality and degenerate equality constraints, we present primal necessary conditions and Kuhn–Tucker type dual necessary conditions under a new constraint qualification. The effectiveness of our results is illustrated on some examples.

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Acknowledgements

The author would like to thank the anonymous reviewers for their valuable suggestions.

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  1. Mathematics Department, University of Pittsburgh at Johnstown, Johnstown, PA, 15904, USA

    Elena Constantin

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Correspondence to Elena Constantin.

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Constantin, E. Necessary conditions for weak efficiency for nonsmooth degenerate multiobjective optimization problems. J Glob Optim 75, 111–129 (2019). https://doi.org/10.1007/s10898-019-00807-9

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